We compute by envelope function calculations the binding energy EB of donor atoms in thin slabs of semiconductor bounded by air, accounting for the dielectric mismatch between air and the semiconductor. We detail how EB depends on the donor-site and on the thickness of the slab. We show that due to the competition between surface and dielectric mismatch effects, EB does not monotonically decrease from the center to the surface of the nanostructures. Finally, we discuss our results in regard to recent photoluminescence experiments performed on ensemble and single GaN nanowires.